Rummenigge: Bayern defender to Sagnol
"I spoke to Willy on Wednesday and he told me it made no sense because no matter how he trained, he always felt pain in his Achille's tendon," Rummenigge told German daily Sueddeutsche Zeitung's website.
"Therefore we can only show understanding when a player tells us 'I quit'", Rummenigge added.
Sagnol's decision was no surprise after Bayern team manager Uli Hoeness had said on Monday he expected the Frenchman to retire.
The 31-year-old Sagnol, who has a contract with the German champions until 2010, should officially announce his retirement at a news conference shortly, Rummenigge added.
Sagnol, who underwent surgery before the start of the season after an already injury-plagued previous year, has not played a competitive match since France's early exit from Euro 2008.
A solid defender capped 58 times by France, he has been with Bayern since 2000, winning the Champions League the following year.
A 2006 World Cup runner-up, Sagnol has also won the German championship five times and the German Cup four times. He started his career at St Etienne, his birthplace, before moving to Monaco, winning the French title with the principality team in 2000.